Fractal Analysis of Four Popular Ghazals Using Method of Distinguishing Styles

This paper delved into the fractal analysis of musical notes in ghazals, exploring the potential existence of self-repeating patterns within the sequences of notes. Ghazals, known for their nuanced melodies and emotional depth, serve as an interesting domain for this exploration.

Our focus lies on the fractal characteristics of four ghazals: Tumko Dekha Toh Ye Khayal Aya, Baat Nikalegi Toh Fir, Jhuki-jhuki Si Nazar, and Tum Itna Jo Muskura Rahe Ho. Each ghazal, based on a distinct raga, provides a unique musical landscape for fractal analysis. The methodology involves collecting details of musical notes, calculating intervals between successive notes, and determining the frequency distribution of these intervals. Fractal analysis is conducted by plotting logarithms of intervals,i.e., ln(I) against logarithms of frequencies, i.e., ln(F), revealing the potential fractal nature of the musical compositions. The results indicate varying degrees of fractal nature among the selected ghazals. While the ghazals "Baat Nikalegi Toh Fir” and "Jhuki Jhuki Si Nazar" exhibit prominent fractal nature with 0.8653 and 0.8319 as the R2 values, the ghazal "Tum Itna Jo Muskura Rahe Ho" with R2 value 0.5408 shows a moderate fractal characteristic and the ghazal "Tumko Dekha Toh Ye" has negligible fractal nature with R2 = 0.2706.

This research contributes to the understanding of the underlying complexity and self-similarity in the arrangement of musical notes within ghazals. Fractal analysis of musical notes provides valuable insights into the organisation of these compositions, offering a unique perspective on the intricate patterns inherent in the world of music.